JRC for Logic
Tsinghua University – University of Amsterdam Joint Research Centre for Logic
JRC for Logic
Tsinghua University – University of Amsterdam Joint Research Centre for Logic

Team Semantics: Linguistic and Philosophical Applications

  • Time: 9:50 AM-12:15 PM, 8th July-12th July
  • Location: Room 3104, Teaching Building No.3, Tsinghua University
  • Lecturer: Maria Aloni (University of Amsterdam)
  • Teaching Assistants: Jialiang Yan (jialiang_yan@mail.tsinghua.edu.cn), Yiqian Wang (yiqian_wang@g.harvard.edu)
  • On-campus course name and course number: 逻辑学专题与前沿（00692241-90）

Maria Aloni

Course Description

In team semantics, formulas are interpreted with respect to a set of points of evaluation (a team) rather than single points. These evaluations points can be valuations (propositional team logic), first order assignments (first-order team semantics) or possible worlds (team-based modal logic).

Historically, team semantics was originally introduced by Hodges (1997) as a compositional semantics for Independence-friendly Logic (Hintikka, Sandu 1989) and later further developed in Dependence Logic (Väänänen 2007), with applications in many areas (database theory, quantum theory, networks, and more).
Inquisitive Semantics (Ciardelli and Roelofsen 2011, Ciardelli, Groenendijk, Roelofsen 2018), developed to account for question meaning, can also be viewed as an example of a team-based system since it evaluates formulas with respect to information states, characterised as sets of possible worlds. Bilateral State-Based Modal Logic (BSML) (Aloni 2022), developed to account for free choice phenomena in natural language, is a recent example of a team-based modal logic merging elements from Dependence Logic and Inquisitive Logic.

In the course, we will provide an overview of different team-based systems, including BSML and extensions of Dependence Logic and Inquisitive Logic, with a focus on their linguistic and philosophical applications.

Tentative Schedule

Day 1. Introduction to team semantics

After a historical overview we will give a first introduction to the following team-based systems: Dependence Logic (Väänänen 2007); Inquisitive Logic (Ciardelli & Roelofsen 2011); Propositional Team Logic (Yang & Väänänen 2017) and Bilateral State-based Modal Logic (Aloni 2022); and discuss some of their formal properties.

Day 2. Bilateral State-based Modal Logic (BSML)

We will delve deeper into BSML and discuss a number of applications, including free choice and ignorance inferences (with comparison with the standard Neo-Gricean implicature account); epistemic contradictions and the acquisition of disjunction.


Day 3. Quantified BSML (qBSML)

In the first part we will present a first order version of BSML (Aloni and Ormondt 2023) and discuss more applications including modified numerals, and distributive inferences. In the second part, dr. Jialiang Yan will give a guest lecture presenting his recent work on epistemic modalities using extensions of BSML.


Day 4: Inquisitive Epistemic Logic

We will focus on Inquisitive Semantics and their account of question meanings and then introduce Inquisitive Epistemic Logic (Ciardelli and Roelofsen, 2011, 2015) and discuss applications in the semantics of inquisitive attitude verbs.


Day 5: Two-sorted Dependence Logic

We will introduce a two-sorted dependence logic with dependence, variation and inclusion atoms and discuss an application to capture cross-linguistic variations in the expression of indefinite reference and specificity (Aloni and Degano 2022, 2024)

Background Knowledge

The material covered in this course is in the interface between philosophical logic and formal semantics. The goal is to make this material accessible to a broad audience, but some familiarity with the syntax and semantics of first-order predicate logic and modal logic is required.


References

  1. Aloni, M. (2022). “Logic and Conversation: the case of Free Choice”. Semantics and Pragmatics, 15(5).
    DOI: https://doi.org/10.3765/sp.15.5
  2. Aloni, M. and Degano, M. (2022). “(Non-)specificity across languages: constancy, variation, v-variation”. Proceedings of Semantic and Linguistic Theory (SALT) 32. URL: https://journals.linguisticsociety.org/proceedings/index.php/SALT/article/view/32.010
  3. Aloni, M, Anttila, A, and Yang, F. (2023). “State-based Modal Logics for Free Choice.” Manuscript, University of Amsterdam.
    URL: https://arxiv.org/abs/2305.11777
  4. Aloni, M. and Degano, M. (2024). How to be (non-)specific. Manuscript, University of Amsterdam.
  5. Aloni, M and Ormondt, P van. (2023). “Modified numerals and split disjunction: the first-order case.” Journal of Logic Language and Information 32, 539–567. DOI: https://doi.org/10.1007/s10849-023-09399-w
  6. Anttila, A. (2021). The Logic of Free Choice Axiomatizations of State-based Modal Logics. MSc Logic Thesis. University of Amsterdam.
  7. Brasoveanu, A., Farkas, D.F. (2011) “How indefinites choose their scope”. Linguistic and Philosophy 34, 1–55. DOI: 10.1007/s10988-011-9092-7
  8. Ciardelli, I., Groenendijk J. and F. Roelofsen (2018). Inquisitive Semantics. Oxford University Press.
  9. Ciardelli, I. and F. Roelofsen (2011). “Inquisitive Logic“. Journal of Philosophical Logic, 40(1):55–94.
  10. Ciardelli, I. and F. Roelofsen (2015). “Inquisitive Dynamic Epistemic Logic“. Synthese, 192(6):1643–1687.
  11. Galliani, P. (2021), “Dependence Logic”, The Stanford Encyclopedia of Philosophy. URL: plato.stanford.edu/entries/logic-dependence/
  12. Hintikka, J. and Sandu G. (1989), “Informational independence as a semantical phenomenon”, in Logic, Methodology and Philosophy of Science VIII (J. E. Fenstad, et al., eds.), North-Holland, Amsterdam, DOI: 10.1016/S0049-237X(08)70066-1
  13. Hodges, W. (1997), “Compositional Semantics for a Language of Imperfect Information”, Logic Journal of the IGPL, 5(4): 539–563. DOI: 10.1093/jigpal/5.4.539
  14. Lück, M. (2020). Team logic: axioms, expressiveness, complexity. Hannover : Gottfried Wilhelm Leibniz Universität. PhD Thesis. DOI: 10.15488/9376
  15. Väänänen, J. (2007), Dependence Logic: A New Approach to Independence Friendly Logic, (London Mathematical Society student texts, 70), Cambridge: Cambridge University Press. DOI: 10.1017/CBO9780511611193
  16. Yang, F., and Väänänen, J. (2017). “Propositional team logics.” Annals of Pure and Applied Logic 168.7: 1406-1441. DOI: 10.1016/j.apal.2017.01.007

Slides and Exercises

Day 1: Tsinghua24Day1

The first time exercises need to be submitted before the class on Wednesday.

Day 2: Tsinghua24Day2

Day 3: Tsinghua24Day3

Day 4: Tsinghua24Day4

Day 5: Tsinghua24Day5

The second time exercises need to be submitted before 24:00 Friday of 12th.

Final exam: Exam

The exam should be submitted before 24:00 Monday of 15th.